NBT-Generalize+place+value+understanding+for+multi-digit+whole+numbers

Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. 4.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. 4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place. || ===‍‍‍‍‍‍Anchor Standard/Mathematical Practice(s) === MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.6. Attend to precision. MP.7. Look for and make use of structure. || Use technology tools and skills to reinforce classroom concepts and activities. || ===‍‍‍‍‍‍Revised Bloom's Level of thinking === Understanding Analyzing || ===‍‍‍‍‍‍Learning Target/Task Analysis === 4.NBT.1 This standard calls for students to extend their understanding of place value related to multiplying and dividing by multiples of 10. In this standard, students should reason about the magnitude of <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">digits in a number. Students should be given opportunities to reason and analyze the <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">relationships of numbers that they are working with. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How is the 2 in the number 582 similar to and different from the 2 in the number 528? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students should be familiar with and use place value as they work with numbers. Some activities <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">that will help students develop understanding of this standard are: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Investigate the product of 10 and any number, then justify why the number now has a 0 at <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">the end. (7 x 10 = 70 because 70 represents 7 tens and no ones, 10 x 35 = 350 because <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">the 3 in 350 represents 3 hundreds, which is 10 times as much as 3 tens, and the 5 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">represents 5 tens, which is 10 times as much as 5 ones.) While students can easily see the <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">pattern of adding a 0 at the end of a number when multiplying by 10, they need to be able <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">to justify why this works. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Investigate the pattern, 6, 60, 600, 6,000, 60,000, 600,000 by dividing each number by <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">the previous number. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Misconceptions <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">There are several misconceptions students may have about writing numerals from verbal <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">descriptions. Number4s like one thousand do not cause a problem; however a number like one <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">thousand two causes problems for students. Many students will understand the 1000 and the 2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">but then instead of placing the 2 in the ones place, students will write the numbers as they hear <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">them, 10002 (ten thousand two). There are multiple strategies that can be used to assist with this <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">concept, including place-value boxes and vertical-addition method. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students often assume that the first digit of a multi-digit number indicates the "greatness" of a <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">number. The assumption is made that 954 is greater than 1002 because students are focusing on <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">the first digit instead of the number as a whole. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4.NBT.2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard refers to various ways to write numbers. Students should have flexibility with the <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">different number forms. Traditional expanded form is 285 = 200 + 80 + 5. Written form is two <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">hundred eighty-five. However, students should have opportunities to explore the idea that 285 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">could also be 28 tens plus 5 ones or 1 hundred, 18 tens, and 5 ones. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students should also be able to compare two multi-digit whole numbers using appropriate <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">symbols. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">The expanded form of 275 is 200 + 70 + 5. Students use place value to compare numbers. For <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">example, in comparing 34,570 and 34,192, a student might say, both numbers have the same <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">value of 10,000s and the same value of 1000s however, the value in the 100s place is different so <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">that is where I would compare the two numbers. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4.NBT.3 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard refers to place value understanding, which extends beyond an algorithm or <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">procedure for rounding. The expectation is that students have a deep understanding of place <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">value and number sense and can explain and reason about the answers they get when they <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">round. Students should have numerous experiences using a number line and a hundreds chart as <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">tools to support their work with rounding. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Your class is collecting bottled water for a service project. The goal is to collect 300 bottles of <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">water. On the first day, Max brings in 3 packs with 6 bottles in each container. Sarah wheels in 6 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">packs with 6 bottles in each container. About how many bottles of water still need to be collected?
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Common Core Standards ===
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Information Technology Standard ===

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Student 1 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">First, I multiplied 3 and 6 which <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">equals 18. Then I multiplied 6 and 6 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">which is 36. I know 18 plus 36 is <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">about 50. I’m trying to get to 300. 50 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">plus another 50 is 100. Then I need 2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">more hundreds. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">So we still need 250 bottles. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Student 2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">First, I multiplied 3 and 6 which <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">equals 18. Then I multiplied 6 and <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">6 which is 36. I know 18 is about <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">20 and 36 is about 40. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">40+20=60. 300- 60 = 240, so we <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">need about 240 more bottles.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍I can...
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can identify the location of a digit in a number. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can determine the value of a digit in a number. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can explain the relationship between the location of a digit and its value. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can demonstrate the value of a number using a variety of tools. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can read and write multi digit whole numbers. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can compare multi digit whole numbers. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can round multi digit whole numbers. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can explain how a multi digit number is rounded to a specific place value.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Essential Vocabulary ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">place value, digit, ones, tens, hundreds, thousands, million, ten times, expanded form, standard form, written form, compare, inequality, >, <, =, symbols, comparisons, round, about, approximately ===

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Sample Assessments
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">miles on the third day. How many total miles did they travel? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Round 368 to the nearest hundred. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This will either be 300 or 400, since those are the two hundreds before and after 368. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Draw a number line, subdivide it as much as necessary, and determine whether 368 is closer to <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">300 or 400. Since 368 is closer to 400, this number should be rounded to 400 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example or reasoning: Round 76,398 to the nearest 1000. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Step 1: Since I need to round to the nearest 1000, then the answer is either 76,000 or <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">77,000. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Step 2: I know that the halfway point between these two numbers is 76,500. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Step 3: I see that 76,398 is between 76,000 and 76,500. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Step 4: Therefore, the rounded number would be 76,000.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Intervention:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students will make a place value chart using paper and highlighters.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Have students make checkbooks with a beginning balance and allow them to earn additional deposits. Students write checks to rent desks, use pencil sharpeners, purchase construction paper and etc. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Use balance scales to compare numbers (found in Foss kit) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Use a deck of cards to practice place value, making biggest/smallest number, etc.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">media type="custom" key="19629202"

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Enrichment:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students create and solve real world word problems.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Bring in guests from local business community (banker, grocery store manager, etc.) to explain how they use rational numbers. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Given story problems work with a partner to create flash cards breaking multi-step problems down into each step.


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===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Notes and Additional Information ===